Matrix analysis
The anatomy of a large-scale hypertextual Web search engine
WWW7 Proceedings of the seventh international conference on World Wide Web 7
Clustering in large graphs and matrices
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Pass efficient algorithms for approximating large matrices
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Fast monte-carlo algorithms for finding low-rank approximations
Journal of the ACM (JACM)
Fast Monte Carlo Algorithms for Matrices II: Computing a Low-Rank Approximation to a Matrix
SIAM Journal on Computing
IEEE/ACM Transactions on Networking (TON) - Special issue on networking and information theory
On the Nyström Method for Approximating a Gram Matrix for Improved Kernel-Based Learning
The Journal of Machine Learning Research
Fast computation of low-rank matrix approximations
Journal of the ACM (JACM)
Automatica (Journal of IFAC)
A decentralized algorithm for spectral analysis
Journal of Computer and System Sciences
Graph sparsification by effective resistances
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Matrix completion from a few entries
IEEE Transactions on Information Theory
Distributed rating prediction in user generated content streams
Proceedings of the fifth ACM conference on Recommender systems
Hi-index | 0.00 |
Eigenvectors of data matrices play an important role in many computational problems, ranging from signal processing to machine learning and control. For instance, algorithms that compute positions of the nodes of a wireless network on the basis of pairwise distance measurements require a few leading eigenvectors of the distances matrix. While eigenvector calculation is a standard topic in numerical linear algebra, it becomes challenging under severe communication or computation constraints, or in absence of central scheduling. In this paper we investigate the possibility of computing the leading eigenvectors of a large data matrix through gossip algorithms. The proposed algorithm amounts to iteratively multiplying a vector by independent random sparsification of the original matrix and averaging the resulting normalized vectors. This can be viewed as a generalization of gossip algorithms for consensus, but the resulting dynamics is significantly more intricate. Our analysis is based on controlling the convergence to stationarity of the associated Kesten-Furstenberg Markov chain.